Flight Instructor reported the student landed instead of doing a touch-and-go as cleared resulting ATC directing an aircraft on approach to going around.

Narrative

I was doing traffic pattern training with my commercial student that recently failed his commercial checkride. I have been moving from my current apartment to another location and did not have the proper rest that I should have and the flight was scheduled for XA:00. On our second to last landing I communicated with the student that the next landing was going to be a 'full stop'. Since I was flying with my commercial student and felt tired; I lost focus of the communication exchange that my student and ATC where having. I did not hear when my student communicated the landing intentions. We landed and my student started to slow down to clear out of the runway. As we rolled down the runway ATC cleared an aircraft for take off but once noticing that we were slow; he asked if we were a 'full stop' to which I replied 'Affirmative'. ATC proceeded to quickly cancel the takeoff clearance and made the landing traffic go around. After reviewing the incident I noticed that my student never requested a 'full stop' and when ATC cleared us to land he firmly said: 'you are cleared for touch and go' and my student replied with 'cleared for touch and go'.I believed that my lack of awareness in this situation played a vital role. I understand that I should not have lost my focus even though I thought that my student would not have made that mistake. Additionally I should have followed the 'IAMSAFE' checklist and not go and postpone the flight since I was feeling tired.What I will do for all my flights is to emphasize the importance of the 'IAMSAFE' checklist and in the event that I would fail an item of the checklist; cancel or postpone the flight immediately and not take any chances of causing a fatal mistake. Additionally I will not lose my focus regardless of whom am I flying with and how simple the task is. I understand that we are all human and we tend to make mistakes.I would like to add a praise to the Tower controller at the time of the incident in ZZZ. His fast reaction to divert traffic and cancel the takeoff clearance helped prevent any major incidents or even an accident.